Conjectures for large N N=4N=4 superconformal chiral primary four point functions

An expression for the four point function for 12-BPS operators belonging to the [0,p,0][0,p,0]SU(4)SU(4) representation in N=4N=4 superconformal theories at strong coupling in the large N limit is suggested for any p  . It is expressed in terms of the four point integrals defined by integration over AdS5AdS5 and agrees with, and was motivated by, results for p=2,3,4p=2,3,4 obtained via the AdS/CFT correspondence. It is assumed all long multiplets gain an anomalous dimension in the large N   limit to leading order in 1/N21/N2. Using crossing symmetry and unitarity, the detailed form is then dictated by the requirement that at large N the contribution of long multiplets with twist less than 2p  , and which, if present in the operator product expansion for two [0,p,0][0,p,0]12-BPS operators would not have anomalous dimensions, should be absent. This requires a non-trivial cancellation with corresponding free field contributions.